English

On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series

Classical Analysis and ODEs 2022-04-05 v1 Functional Analysis Representation Theory Spectral Theory

Abstract

We discuss the spectral decomposition of the hypergeometric differential operators on the line Rez=1/2\mathrm{Re}\, z=1/2. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal covering of the group SL(2RSL(2\,{\mathbb R}. Our main purpose is a search of natural bases in generalized eigenspaces and variants of the inversion formula.

Keywords

Cite

@article{arxiv.2105.10800,
  title  = {On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series},
  author = {Yury A. Neretin},
  journal= {arXiv preprint arXiv:2105.10800},
  year   = {2022}
}

Comments

16p

R2 v1 2026-06-24T02:22:30.631Z